.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here ` to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_numerical_methods_optimization_plot_minmax_optimization.py:
Mix/max search using optimization
=================================
In this example we are going to evaluate the min and max values of the output variable of interest in a domain using an optimization algorithm.
.. code-block:: default
from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
ot.Log.Show(ot.Log.NONE)
Create the marginal distributions of the parameters
.. code-block:: default
dist_E = ot.Beta(0.93, 2.27, 2.8e7, 4.8e7)
dist_F = ot.LogNormalMuSigma(30000, 9000, 15000).getDistribution()
dist_L = ot.Uniform(250, 260)
dist_I = ot.Beta(2.5, 1.5, 3.1e2, 4.5e2)
marginals = [dist_E, dist_F, dist_L, dist_I]
distribution = ot.ComposedDistribution(marginals)
Define bounds
.. code-block:: default
lowerBound = [marginal.computeQuantile(0.1)[0] for marginal in marginals]
upperBound = [marginal.computeQuantile(0.9)[0] for marginal in marginals]
bounds = ot.Interval(lowerBound, upperBound)
Create the model
.. code-block:: default
model = ot.SymbolicFunction(['E', 'F', 'L', 'I'], ['F*L^3/(3*E*I)'])
Define the problems
.. code-block:: default
minProblem = ot.OptimizationProblem(model)
minProblem.setBounds(bounds)
maxProblem = ot.OptimizationProblem(model)
maxProblem.setBounds(bounds)
maxProblem.setMinimization(False)
Create a solver
.. code-block:: default
solver = ot.TNC()
solver.setStartingPoint(distribution.getMean())
Solve the problems
.. code-block:: default
solver.setProblem(minProblem)
solver.run()
minResult = solver.getResult()
print('min: y=', minResult.getOptimalValue(), 'with x=', minResult.getOptimalPoint())
solver.setProblem(maxProblem)
solver.run()
maxResult = solver.getResult()
print('max: y=', maxResult.getOptimalValue(), 'with x=', maxResult.getOptimalPoint())
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
min: y= [6.37642] with x= [4.04419e+07,21319.7,251,435.785]
max: y= [23.4246] with x= [2.87477e+07,41178.7,259,354.141]
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 0.004 seconds)
.. _sphx_glr_download_auto_numerical_methods_optimization_plot_minmax_optimization.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_minmax_optimization.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_minmax_optimization.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_